al-Wali and al-Mawla are two of the names of Allah, because Allah, may He be exalted, says (interpretation of the meaning):
“Or have they taken (for worship) Awliya (guardians, supporters, helpers, protectors, etc.) besides Him? But Allah, He Alone is the Wali (Protector, etc.). And it is He Who gives life to the dead, and He is Able to do all things”
“Allah is the Wali (Protector or Guardian) of those who believe. He brings them out from darkness into light”
“And if they turn away, then know that Allah is your Mawla (Patron, Lord, Protector and Supporter, etc.), (what) an Excellent Mawla, and (what) an Excellent Helper!”
“Pardon us and grant us Forgiveness. Have mercy on us. You are our Mawla (Patron, Supporter and Protector, etc.) and give us victory over the disbelieving people”
“Say: Nothing shall ever happen to us except what Allah has ordained for us. He is our Mawla (Lord, Helper and Protector)." And in Allah let the believers put their trust”
And the Prophet (blessings and peace of Allah be upon him) said:
“You are its Guardian (Wali) and its Lord (Mawla).”
Narrated by Muslim, 7081
See: Fayd al-Qadeer, 2/613; al-Qawaa’id al-Mathla, p. 15
It is permissible to call another person “mawlana” if he is Muslim, but it is not permissible to say that to a disbeliever.
Some of the scholars said that it is permissible to use the word mawla to refer to a Muslim who is distinguished in knowledge or righteousness.
The Prophet (blessings and peace of Allah be upon him) said to Zayd ibn Haarithah: “You are our brother and our mawla.”
Narrated by al-Bukhaari, 2552
The word mawla may be used with reference to an owner, companion, relative, neighbour, ally, supporter, lover, benefactor, recipient of kindness, slave or freed slave. See: al-Qamoos al-Muheet.
Ibn al-Atheer said: The word mawla appears frequently in hadeeth. It is a word that may be applied to many things. It may refer to the Lord, the owner, the master, the benefactor, the freed slave, the supporter, the lover, the follower, the neighbour, the cousin, the ally, the son-in-law, the slave, the freed slave, and the recipient of kindness. It mostly appears in hadeeth and should be interpreted according to the context of the hadeeth in which it is mentioned. Everyone who is in charge of a matter or undertakes a matter may be described as its mawla or wali.
End quote from an-Nihaayah fi Ghareeb al-Hadeeth, 5/227
Hence there is nothing wrong with giving this name to a person so long as he is not a disbeliever.
Ibn al-Qayyim (may Allah have mercy on him) said: Section: The dhimmi cannot be addressed as Sayyiduna etc
With regard to addressing (the dhimmi) as sayyiduna, mawlana and the like (titles roughly meaning “our master”), that is definitely haraam.
End quote from Ahkaam Ahl adh-Dhimmah, 2/771
An-Nawawi said: Imam Abu Ja‘far an-Nahhaas said in his book Sinaa‘at al-Kitaab: With regard to the word al-mawla, we do not know of any difference of opinion among the scholars concerning the fact that no one should say “mawlaya (my master)” to another person. But I say: We have seen in the previous chapter that it is permissible in all cases to say mawlaya and there is no difference between (the two forms of the word). an-Nahhaas was speaking of the word with the definite article (al-mawla). Similarly, an-Nahhaas said: The word sayyid may be said to anyone who is not an evildoer, but it should not be used with the definite article (as-sayyid) to refer to anyone other than Allah, may He be exalted. But the more correct view is that there is nothing wrong with saying al-mawla and as-sayyid (with the definite article, with reference to people) subject to the conditions mentioned above, i.e., a person may becalled as-sayyid (with the definite article) if he is a person of virtue and goodness, either because of his knowledge or his righteousness and so on. If he is an evildoer or there is some doubt concerning his religious commitment and the like, it is makrooh to call him sayyid.
End quote from al-Adhkaar, p. 840. See also Mu‘jam al-Manaahi al-Lafziyyah, p. 535
And Allah knows best.